Finite Group Databasebeta

← Group #6875

Character table — Group #6875

Order 243.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35
size11133333333999999999999999999999999
order13333999999999999272727272727272727272727272727272727
χ111111111111111111111111111111111111
χ211111111111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ311111111111111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32
χ411111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32
χ511111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111−1−i32−1−i32−1−i32111−1+i32−1+i32−1+i32
χ611111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111
χ711111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32
χ811111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111
χ911111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111−1+i32−1+i32−1+i32111−1−i32−1−i32−1−i32
χ10111−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32ζζ4ζ7ζ2ζ5ζ81−1+i32−1−i32ζζ4ζ7ζ2ζ5ζ81−1+i32−1−i32ζζ4ζ7ζ2ζ5ζ8
χ11111−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32ζζ4ζ7ζ2ζ5ζ8−1+i32−1−i321ζ4ζ7ζζ5ζ8ζ2−1−i321−1+i32ζ7ζζ4ζ8ζ2ζ5
χ12111−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32ζζ4ζ7ζ2ζ5ζ8−1−i321−1+i32ζ7ζζ4ζ8ζ2ζ5−1+i32−1−i321ζ4ζ7ζζ5ζ8ζ2
χ13111−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32ζ4ζ7ζζ8ζ2ζ51−1+i32−1−i32ζ4ζ7ζζ8ζ2ζ51−1+i32−1−i32ζ4ζ7ζζ8ζ2ζ5
χ14111−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32ζ4ζ7ζζ8ζ2ζ5−1+i32−1−i321ζ7ζζ4ζ2ζ5ζ8−1−i321−1+i32ζζ4ζ7ζ5ζ8ζ2
χ15111−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32ζ4ζ7ζζ8ζ2ζ5−1−i321−1+i32ζζ4ζ7ζ5ζ8ζ2−1+i32−1−i321ζ7ζζ4ζ2ζ5ζ8
χ16111−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32ζ7ζζ4ζ5ζ8ζ21−1+i32−1−i32ζ7ζζ4ζ5ζ8ζ21−1+i32−1−i32ζ7ζζ4ζ5ζ8ζ2
χ17111−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32ζ7ζζ4ζ5ζ8ζ2−1+i32−1−i321ζζ4ζ7ζ8ζ2ζ5−1−i321−1+i32ζ4ζ7ζζ2ζ5ζ8
χ18111−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32ζ7ζζ4ζ5ζ8ζ2−1−i321−1+i32ζ4ζ7ζζ2ζ5ζ8−1+i32−1−i321ζζ4ζ7ζ8ζ2ζ5
χ19111−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32ζ2ζ8ζ5ζ4ζζ71−1−i32−1+i32ζ2ζ8ζ5ζ4ζζ71−1−i32−1+i32ζ2ζ8ζ5ζ4ζζ7
χ20111−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32ζ2ζ8ζ5ζ4ζζ7−1+i321−1−i32ζ5ζ2ζ8ζ7ζ4ζ−1−i32−1+i321ζ8ζ5ζ2ζζ7ζ4
χ21111−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32ζ2ζ8ζ5ζ4ζζ7−1−i32−1+i321ζ8ζ5ζ2ζζ7ζ4−1+i321−1−i32ζ5ζ2ζ8ζ7ζ4ζ
χ22111−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32ζ5ζ2ζ8ζζ7ζ41−1−i32−1+i32ζ5ζ2ζ8ζζ7ζ41−1−i32−1+i32ζ5ζ2ζ8ζζ7ζ4
χ23111−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32ζ5ζ2ζ8ζζ7ζ4−1+i321−1−i32ζ8ζ5ζ2ζ4ζζ7−1−i32−1+i321ζ2ζ8ζ5ζ7ζ4ζ
χ24111−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32ζ5ζ2ζ8ζζ7ζ4−1−i32−1+i321ζ2ζ8ζ5ζ7ζ4ζ−1+i321−1−i32ζ8ζ5ζ2ζ4ζζ7
χ25111−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32ζ8ζ5ζ2ζ7ζ4ζ1−1−i32−1+i32ζ8ζ5ζ2ζ7ζ4ζ1−1−i32−1+i32ζ8ζ5ζ2ζ7ζ4ζ
χ26111−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32ζ8ζ5ζ2ζ7ζ4ζ−1+i321−1−i32ζ2ζ8ζ5ζζ7ζ4−1−i32−1+i321ζ5ζ2ζ8ζ4ζζ7
χ27111−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32ζ8ζ5ζ2ζ7ζ4ζ−1−i32−1+i321ζ5ζ2ζ8ζ4ζζ7−1+i321−1−i32ζ2ζ8ζ5ζζ7ζ4
χ2833333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32000000000000000000000000
χ2933333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32000000000000000000000000
χ30333−3+3i32−3−3i32−3+3i32−3−3i32−3−3i3233−3+3i32000000000000000000000000
χ31333−3+3i32−3−3i32−3−3i32−3+3i323−3−3i32−3+3i323000000000000000000000000
χ32333−3−3i32−3+3i32−3+3i32−3−3i323−3+3i32−3−3i323000000000000000000000000
χ33333−3−3i32−3+3i32−3−3i32−3+3i32−3+3i3233−3−3i32000000000000000000000000
χ349−9+9i32−9−9i3200000000000000000000000000000000
χ359−9−9i32−9+9i3200000000000000000000000000000000

Here ζ is a primitive root of unity of order 9 (ζ9 = 1); i = ζ2.